Hello Stefano,

long time ago I learnt that it is better not to use variables with a "complicated" structure like Superscript and so on. So it seems to be better to use "simple" expressions.

You could change that like

\[CurlyPhi] = 
 Subscript[x, 1]*Conjugate[Subscript[x, 1]] + 
  Subscript[x, 2]*Conjugate[Subscript[x, 2]] - 
  Subscript[x, 3]*Conjugate[Subscript[x, 3]] - 1

Then

\[CurlyPhi] = \[CurlyPhi] /. {
   Subscript[x, j_] :> ToExpression["x" <> ToString[j]],
   Conjugate[Subscript[x, j_]] :>  ToExpression["x" <> ToString[j] <> "c"]
   }

Your derivative is synthactically wrong. You should write

c = D[\[CurlyPhi], x2, x3c]

I hope this helps.